Paired, active-space treatments of static correlation are augmented with additional amplitudes to produce a hierarchy of parsimonious and efficient cluster truncations that approximate the total energy. The number of parameters introduced in these models grow with system size in a tractable way: two powers larger than the static correlation model it is built upon: for instance cubic for the models built on perfect pairing, fourth order for a perfect quadruples (PQ) reference, and fifth order for the models built on perfect hextuples. These methods are called (SD) corrections to perfect pairing, PQ, perfect hextuples, and two variants are explored. An implementation of the SD methods is compared to benchmark results for and dissociation problems, the and model systems, and the insertion of beryllium into hydrogen. In the cases examined even the quartic number of parameters associated with PQSD is able to provide results which meaningfully improve on coupled-cluster singles doubles (CCSD) (which also has quartic amplitudes) and compete with existing multi-reference alternatives.
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